STATS TCO 1

STATISTICS
CHAPTER 1 NOTES

DATA: consists of information coming from observations, counts, measurements, or responses.

STATISTICS: is the science of collecting, organizing, analyzing, and interpreting data in order to make decisions.

DATA SETS:
-POPULATION: is the collection of all outcomes, responses, measurements or counts that are of interest -SAMPLE: is a subset or part of a population
EXAMPLE OF POPULATION:
The age of each resident in an apartment building

EXAMPLE OF SAMPLE:
The temperature in 4 state capitals out of 50

PARAMETER: is a numerical description of a population characteristic
EXAMPLE OF PARAMETER: the 2182 students who accepted admission offers to Northwestern University in 2008 have an average SAT score of 1442

STATISTIC: is a numerical description of a sample characteristic
EXAMPLE OF STATISTIC: a study of 6076 adults in public restrooms found that 23% did not wash their hands before exiting.

BRANCHES OF STATISTICS -DESCRIPTIVE STATISTICS: is the branch of statistics that involves the organization, summarization, and display of data -INFERENTIAL STATISTICS: is the branch of statistics that involves using a sample to draw conclusions about a population. A basic tool in the study of inferential statistics is probability

TYPES OF DATA -QUALITATIVE DATA: consists of attributes, labels, or nonnumeric entries -QUANTIATIVE DATA: consists of numerical measurements or counts
EXAMPLE OF QUALITATIVE DATA: favorite musical band
EXAMPLE OF QUANTITATIV DATA: number of flights leaving an airport each year

LEVELS OF MEASUREMENT (LOW TO HIGH) -NOMINAL: qualitative data only. Data at this level are categorized using names, labels or quantities. No mathematical computations can be made at this level
EXAMPLE OF NOMINAL: social security numbers, numbers on sports jerseys. (it would not make sense to add sport jerseys together for the Chicago bulls team)

ORDINAL: are qualitative or quantitative. Data at this level can be arranged in order, or ranked, but differences between entries are not meaningful.
EXAMPLE OF ORDINAL: top 5 TV programs: 1. American idol on tuesday 2. American idol on wednesday 3. Dancing with the stars 4. NCIS 5. The mentalist

INTERVAL: data this level can be ordered, and meaningful differences between data entries can be calculated. At this level, a zero entry simply represents a position on a scale, the entry is not an inherent zero.
EXAMPLE OF INTERVAL: temperature outside is 0 celcius. A position on the Celsius scale.
2 degrees is not twice as warm as 1 degree.

RATIO: similar to interval with the added property that a zero entry is an inherent zero. A ratio of two data values can be formed so that the one data value can be meaningful expressed as a multiple of another. (an inherent zero implies “none”)
EXAMPLE OF RATIO: you have zero dollars in your account, meaning you have NO money.
$2.00 is twice as $1.00

LEVEL OF MEASUREMENT
PUT DATA IN CATEGORIES
ARRANGE DATA IN ORDER
SUBTRACT DATA VALUES
DETERMINE IF ONE DATA VALUE IS A MULTIPLE OF ANOTHER
NOMINAL
YES
NO
NO
NO
ORDINAL
YES
YES
NO
NO
INTERVAL
YES
YES
YES
NO
RATIO
YES
YES
YES
YES

LEVEL
EXAMPLE OF A DATA SET
MEANINGFUL CALCULATIONS
NOMINAL LEVEL (QUALITATIVE DATA)
TYPES OF SHOWS TELEVISED BY A NETWORK
COMEDY SPORTS
DRAMA COOKING
REALITY SHOWS SOAPS
DOCUMENTARIES TALK SHOWS
PUT IN A CATEGORY
ORDINAL LEVEL (QUALITATIVE OR QUANTITATIVE DATA)
MOTION PICTURE ASSOCIATION OF AMERICA RATINGS DESCRIPTION
G = GENERAL AUDIENCES
PG = PARENTAL GUIDENACE SUGGESTED
PG-13 PARENTS STRONGLY CAUTIONED
R = RESTRICTED
NC-17 NOBODY UNDER 17 YEARS OF AGE
PUT IN A CATEGORY AND PUT IN ORDER. FOR INSTANCE PG RATING HAS A STRONGER RESTRICTION THAN A G RATING.
INTERVAL LEVEL (QUANTIATIVE DATA)
AVERAGE MONTHLY TEMPS
IN DENVER, COLORADO
JAN 29.2 JULY 73.4
FEB 33.2 AUG 71.7
MAR 39.6 SEP 62.4
APRIL 47.6 OCT 51
MAY 57.2 NOV 37.5
JUN 67.6 DEC 30.3
PUT IN A CATEGORY, PUT IN ORDER, AND FIND DIFFERENCES BETWEEN VALUES. MAY IS WARMER THAN APRIL
RATIO LEVEL (QUANTITATIVE DATA)
AVERAGE MONTHLY PRECIPITATION IN INCHES FOR ORLANDO FLORIDA
PUT IN A CATEGORY, PUT IN ORDER, FIND DIFFERENCES BETWEEN VALUES AND RATIOS
DATA COLLECTIONS AND EXPERIMENTAL DESIGN
-DESIGNING A STATISTICAL STUDY 1. IDENTIFY THE VARIABLE(S) OF INTEREST (THE FOCUS) AND THE POPULATION OF STUDY
2. DEVELOP A DETAILED PLAN FOR COLLECTING DATA. IF YOU USE A SAMPLE MAKE SURE THE SAMPLE IS REPRESENTTIVE OF THE POPULATION
3. COLLECT THE DATA
4. DESCRIBE THE DATA, USING DESCRIPTIVE STATISTICS TECHNIQUES
5. INTERPRET THE DATA AND MAKE DECISIONS ABOUT THE POPULATION USING INFERENTIAL STATISTICS
6. IDENTIFY ANY POSSIBLE ERRORS
-DATA COLLECTION -OBERSERVATIONAL STUDY -PERFORM AN EXPERIMENT -SIMULATION -SURVEY
DATA COLLECTION METHOD
EXAMPLE
OBSERVATIONAL
A STUDY OF HOW 4TH GRADE STUDENTS SOLVE A PUZZLE
EXPERIMENTAL STUDY
A STUDY OF THE EFFECT OF EATING OATMEAL ON LOWERING BLOOD PRESSURE
SIMULATION STUDY
A STUDY OF THE EFFECT OF CHANGING FLIGHT PATTERNS ON THE NUMBER OF AIRPLANE ACCIDENTS
SURVEY STUDY
A STUY OF U.S. RESIDENTS APPROVAL RATING OF THE U.S. PRESIDENT

-EXPERIMENTAL DESIGN -THREE KEY ELEMENTS OF A WELL-DESIGNED EXPERIEMNT ARE CONTROL, RANDOMIZATION, AND REPLICATION
-CONFOUNDING VARIABLE: occurs when an experimenter cannot tell the difference between the effects of different factors on a variable
-PLACEBO EFFECT: when a subject reacts favorably to a placebo when in fact the subject has been given no medicated treatment at all.
-BLINDING: technique where subjects do not know whether they are receiving a treatment or a placebo
-DOUBLE-BLIND EXPERIMENT: neither the subject or experimenter know who has taken the placebo and who has taken the treatment (this is preferred)
-RANDOMIZATION: a process of randomly assigning subjects to different treatment groups
-COMPLETELY RANDOMIZED DESIGN: subjects are assigned to different treatment groups through random selection
-RANDOMIZED BLOCK DESIGN: divide subjects with similar characteristics into blocks, and then, within each block, randomly assign subjects to treatment groups
-MATCHED PAIR DESIGN: where subjects are paired up according to a similarity. One subject in the pair receives one treatment while the other receives another.
-SAMPLE SIZE: which is the number of subjects, is another important part of experimental design. To improve validity of experiment results, replication is required
-REPLICATION: is the repetition of an experiment under the same or similar conditions

SAMPLING TECHNIQUES -CENSUS: is a count or measure of an entire population -SAMPLING: is a count or measure of part of a population
-SAMPLE ERROR: is the difference between the results of a sample and the results of the population
-RANDOM SAMPLE: is one in which every member of the population has an equal chance of being selected
-SIMPLE RANDOM SAMPLE: is a sample in which every possible sample of the same size has the same chance of being selected.
-STRATIFIED SAMPLE: when it is important to have members from each segment of the population
-CLUSTER SAMPLE: when the population falls into naturally occurring subgroups, each having a similar characteristics. Divide the population into clusters
-SYSTEMATIC SAMPLE: in which every member of the population is assigned a number. The membres of the population are ordered in some way, a starting number is selected, and then sample members are selected at regular intervals from the starting number.
-CONVIENCE SAMPLE: consist of only available members of the population

CHAPTER 2 NOTES
FREQUENCY DISTRIBUTIONS AND THEIR GRAPHS
FREQUENCY DISTRIBUTION: is a table that shows classes or intervals of data entries with a count of the number of entries in each class.
EXAMPLE:
CLASS
FREQUENCY f
1-5
5
6-10
8
11-15
6
16-20
8
21-25
5
26-30
4

Upper class limit: 5, 10 15, 20 25, and 30
Lower class limit: 1, 6, 11, 16, 21, and 26
Class width: distance between upper or lower class limits of consecutive classes 6-1=5
Range: difference between max and minimum data entries

CONSTRUCTING A FREQUENCY DISTRIBUTION FROM A DATA SET
1. DECIDE ON THE NUMBER OF CLASSES. SHOULD BE BETWEEN 5 – 20
2. FIND THE CLASS WIDTH AS FOLLOWS. DETERMINE THE RANGE OF DATA, DIVIDE THE RANGE BY THE NUMBER OF CLASSES, AND ROUND UP TO THE NEXT CONVIENT NUMNER
3. FIND THE CLASS LIMITS
4. MAKE A TALLY MARK FOR EACH DATA ENTRY IN THE ROW OF THE APPROPRIATE CLASS
5. COUNT THE TALLY MAKRS TO FIND THE FREQUENCY

EXAMPLE: THE FOLLOWING LISTS THE PRICES IN DOLLARS OF 30 PORTABLE GLOBAL POSITIONING SYSTEM (GPS) NAVIGATORS. CONSTRUCT A FREQUENCY DISTRIBUTION TABLE THAT HAS SEVEN CLASSES

90 130 400 200 350 70 325 250 150 250
275 270 150 130 59 200 160 450 300 130
220 100 200 400 200 250 95 180 170 150

MINIMUM DATA ENTRY = 59
MAXIMUM DATA ENTRY = 450
RANGE= 450 – 59 = 391
DIVIDE RANGE BY NUMBER OF CLASSES 391/7 = 55.86 ROUND UP TO 56
Ef= sum of frequencies (30)
59 + 56 = 115 -1 = 114
59-114 FOR THE FIRST CLASS

CLASS
F
59-114
5 IIIII
115-170
8 IIIIIIII
171-226
6 IIIIII
227-282
5 IIIII
283-338
2 II
339-394
1 I
395-450
3 III
Ef = sum of frequencies (tallys)
Midpoint = Lower class limit + upper class limit divided by 2
Relative Frequency = Class frequency divided by sample size (n) f/n
Cumulative frequency = sum of frequencies of that class and all previous classes. The cumulative frequency of the last class is equal to the sample size n

FREQUENC HISTOGRAM
FRQUENCY HISTORGRAM: is a bar graph that represents the frequency distribution of a data set.
-A historgram as the following properties: 1. The horizontal scale is quantitative and measures the data values 2. the vertical scale measures the frequency of the classes 3. Consecutive bars must touch
-because consecutive bars must touch, bars must begin and end at class boundaries instead of class limits. CLASS BOUNDARIES are the numbers that separate classes without forming gaps between them.
-if data entries are integers, subtract 0.5 from each lower limit to find the lower class boundaries. To find the upper class boundaries add 0.5 to each upper limit. The upper boundary limit of a class will equal the lower boundary of the next higher class

RELATIVE FREQUENCY HISTORGRAM
-HAS THE SAME SHAPE AND THE SAME HORIZONTAL SCALE AS THE CORRESPONDING FREQUENCY HISTORGRAM. THE DIFFERENCE IS THAT THE VERTICAL SCALE MEASURES RELATIVE FREQUENCIES, NOT FREQUENCIES.

GRAPHING QUANTIATIVE DATA SETS
-NEWER WAY TO DISPLAY QUANTITATIVE DATA SETS: STEM AND LEAF PLOT
-In a stem and leaf plot, each number is sepeated by a stem and a leaf. You should have as many leaves as there are entries in the original data set and the leaves should be single digits

MEASURE OF CENTRAL TENDENCY
-MEAN: SUM OF ENTRIES DIVIDED BY NUMBER OF ENTRIES
-MEDIAN: FIRST ORDER THE DATA, THE MEDIAN IS THE MIDDLE NUMBER.
-MODE: NUMBER THAT REPEATS THE MOST. ORDERING DATA HELPS